Bulletin of Dnipropetrovsk University. Series: Communications in Mathematical Modeling and Differential Equations Theory

1-31

Authors: Vladimir L. Borsch, Peter I. Kogut

A 1-parameter initial boundary value problem (IBVP) for a linear homogeneous degenerate wave equation (JODEA, 28(1), 1) in a space-time rectangle is considered. The origin of degeneracy is the power law coefficient function with respect to the spatial distance to the symmetry line of the rectangle, the exponent being the only parameter of the problem, ranging in (0,1) and (1,2) and producing the weak and strong degeneracy respectively. In the case of weak degeneracy separation of variables is used in the rectangle to obtain the unique bounded continuous solution to the IBVP, having the continuous flux. In the case of strong degeneracy the IBVP splits into the two derived IBVPs posed respectively in left and right half-rectangles and solved separately using separation of variables. Continuous matching of the obtained left and right families of bounded solutions to the IBVPs results in a linear integro-differential equation of convolution type. The Laplace transformation is used to solve the equation and obtain a family of bounded solutions to the IBVP, having the continuous flux and depending on one undetermined function.

42-53

Authors: Eteri L. Hart, Bohdan I. Terokhin

Computer simulation of the behavior of a thin elastic rectangular plate with a circular hole and an annular inclusion made of functionally graded material has been carried out. Using the finite element method, the influence of the geometric and mechanical parameters of the inclusion on the concentration of stresses around the hole is investigated and various laws of the change in the modulus of elasticity of a functionally graded material are specified. A comparative analysis of the results has been carried out. The recommendations for reducing stress concentration are given.

79-95

Authors: Aleksandr A. Dzyuba, Anatoliy P. Dzyuba, Larisa D. Levitina, Inga A. Safronova

Well-posed boundary value problems are constructed for calculating rotation shells of with a stiffness variable along the meridian in two directions, and also with variable bilateral with respect to the reference surface with the shell wall thickness. Algorithms for the numerical integration of systems of differential equations with variable coefficients are discussed.